Elon Musk targeted Jeff Bezos shortly before his opponent's maiden voyage yesterday.
Its owner SpaceX, used his Twitter account over the weekend to joke about Bezos' flight plan, which reached more than 60 miles above Earth on a rocket built by his company, Blue Origin.
This is the latest incident, a dispute that has existed for 15 years between the two billionaires.
Rocket companies based in USA are at the forefront of the emerging private space sector and compete for lucrative contracts with Nasa.
Before the Bezos space trip, Musk posted several memes about the Amazon founder and his mission.
Someone made fun of the fact that the launch will reach an altitude of just 62 miles.
While this is the internationally recognized limit of space, it is very far from Earth's orbit, where SpaceX launches usually reach about 250 miles above Earth.
Musk also responded to a tweet referring to a conversation between the two billionaires over a dinner in 2004.
"In 2004, Elon Musk and Jeff Bezos met for a meal, to discuss space. "It was one of their few personal interactions," the tweet began.
Musk has publicly mocked his former colleague, who he once called a "copycat" on Twitter, after Amazon acquired its rival carmaker Tesla, Zoox.
when the with the BBC Asked Musk about the Bezos in 2016, he replied, "Who is Jeff?"
However, on Monday, in response to a tweet about the Bezos flight published by the official Blue Origin account, Musk replied: "Good luck tomorrow"
The reusable New Shepard of Blue Origin flew at an altitude of 62 miles. It was Blue Origin's first human space flight. Bezos, 57, and younger brother Mark, 53, were accompanied by two additional passengers, the 82-year-old wally funk, who trained as an astronaut in the 1960s, but was never given the opportunity to fly the 18-year-old Oliver Daemen, son of the millionaire Joes Daemen.